Finite element analysis of a nematic liquid crystal Landau-de Gennes model with quartic elastic terms
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912029309140992 |
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| author | Elafandi, Jacob Weber, Franziska |
| author_facet | Elafandi, Jacob Weber, Franziska |
| contents | In arXiv:1906.09232v2, Golovaty et al. present a $Q$-tensor model for liquid crystal dynamics which reduces to the well-known Oseen-Frank director field model in uniaxial states. We study a closely related model and present an energy stable scheme for the corresponding gradient flow. We prove the convergence of this scheme via fixed-point iteration and rigorously show the $Γ$-convergence of discrete minimizers as the mesh size approaches zero. In the numerical experiments, we successfully simulate isotropic-to-nematic phase transitions as expected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite element analysis of a nematic liquid crystal Landau-de Gennes model with quartic elastic terms Elafandi, Jacob Weber, Franziska Numerical Analysis 65M60 In arXiv:1906.09232v2, Golovaty et al. present a $Q$-tensor model for liquid crystal dynamics which reduces to the well-known Oseen-Frank director field model in uniaxial states. We study a closely related model and present an energy stable scheme for the corresponding gradient flow. We prove the convergence of this scheme via fixed-point iteration and rigorously show the $Γ$-convergence of discrete minimizers as the mesh size approaches zero. In the numerical experiments, we successfully simulate isotropic-to-nematic phase transitions as expected. |
| title | Finite element analysis of a nematic liquid crystal Landau-de Gennes model with quartic elastic terms |
| topic | Numerical Analysis 65M60 |
| url | https://arxiv.org/abs/2409.09837 |